Police said the man, identified as Ali Syed, 20, of Ladera Ranch, Calif., told one of his victims, whose car he stole: "I killed somebody. This is my last day."

In all, there were three homicide victims and at least five victims of attempted homicide, police said.

Syed, a student at Saddleback College in Mission Viejo with no criminal record, shot and killed a young woman in his home in Ladera Ranch, which he shared with his parents, said Scott Jordan, police chief of the town of Tustin, where several of the incidents occurred Tuesday.

The relationship between Syed and the young woman remained unclear, as was the reason she was in the home, police said.

Syed's parents were home at the time, about 4:45 a.m. (7:45 a.m. ET), and fled, Jordan said. Syed then took their black sport-utility vehicle and set out on a drive along Orange County's highways, stopping at times to change cars and shoot people — apparently at random, according to police.

As state troopers homed in on him, he then killed himself.

Police and sheriff's officials gave this account of the dramatic chase:

Syed's first stop was the parking lot of a restaurant in Tustin, another Los Angeles suburb about 20 miles away, where he was spotted loading his shotgun by a man who was waiting in his car for his son.

The man quickly drove off with Syed chasing him on foot and firing his shotgun. The man was shot in the back of head but survived and managed to drive a short way before coming to a stop. Syed shot and wounded a second person who had rushed up to see what was happening.

Syed's car was damaged and had a flat tire, so he ran across the street to a gasoline station, where he approached a man filling up his tank. He took the man's truck after politely telling him: "I don't want to hurt you. I killed somebody. This is my last day. Give me your keys."

Investigators update the deadly carjackings in Southern California.

Now in his second stolen vehicle, Syed took off down state Route 55. He exited in Santa Ana, where he began randomly firing at vehicles on the freeway.

Three vehicles were damaged in Santa Ana, the driver of one of which suffered minor injuries to his face and hand. That man drove home and called police, who began tracking Syed in earnest. The drivers of all three damaged vehicles were being considered victims of attempted homicide.

Back in the stolen truck, Syed again tore off down Route 55. He took an off-ramp too fast, causing him to jump the curb, whereupon he leapt out of the truck, approached a man who was stopped at a stop sign, "walked him across the road and executed him, shooting him three times," Jordan said.

That victim was identified as Melvin Lee Edwards, 69, of Laguna Hills.

Syed then took the man's BMW — his third stolen vehicle — and drove off to the parking lot of a computer store, where he shot two people, apparently strangers, killing one of them. The dead man was identified as Jeremy Lewis, 26, of Fullerton.

Syed drove off in yet another stolen vehicle, returning to Route 55 as emergency calls poured in to authorities. As state troopers were preparing to get into position, he exited the freeway in the city of Orange. With the stolen vehicle still moving, he jumped out, put the shotgun to his head and killed himself.

Authorities said they found the shotgun beside Syed's body. And as of late Tuesday afternoon, they said, they had no explanation for why any of it happened.

Matthew DeLuca and Olivia Santini of NBC News contributed to this report. Follow M. Alex Johnson on Twitter and Facebook.